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In [13], K. Roth showed that the expected value of the $L^2$ discrepancy of the cyclic shifts of the $N$ point van der Corput set is bounded by a constant multiple of $sqrt{log N}$, thus guaranteeing the existence of a shift with asymptotically minimal $L^2$ discrepancy, [11]. In the present paper, we construct a specific example of such a shift.
The van der Waals heterostructures are a fertile frontier for discovering emergent phenomena in condensed matter systems. They are constructed by stacking elements of a large library of two-dimensional materials, which couple together through van der
In inhomogeneous dielectric media the divergence of the electromagnetic stress is related to the gradients of varepsilon and mu, which is a consequence of Maxwells equations. Investigating spherically symmetric media we show that this seemingly unive
In this article we explicitly describe irreducible trinomials X^3-aX+b which gives all the cyclic cubic extensions of Q. In doing so, we construct all integral points (x,y,z) with GCD(y,z)=1, of the curves X^2+3Y^2 = 4DZ^3 and X^2+27Y^2=4DZ^3 as D va
Let $G$ be a finite abelian group. We say that $M$ and $S$ form a textsl{splitting} of $G$ if every nonzero element $g$ of $G$ has a unique representation of the form $g=ms$ with $min M$ and $sin S$, while $0$ has no such representation. The splitt
The van der Waals quintessence equation of state is an interesting scenario for describing the late universe, and seems to provide a solution to the puzzle of dark energy, without the presence of exotic fluids or modifications of the Friedmann equati